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FAQ: Fixed Angle

How do I construct an angle of fixed magnitude (e.g., 33 degrees)?

Occasionally, you may wish to create an angle of fixed measure (for instance, an angle that measures exactly 33 degrees). While you could create an angle by measuring three points and dragging them until they form an angle of 33 degrees, this angle would not be constructed to be exactly 33 degrees. That is, dragging it again would change it from its current magnitude to some other magnitude.

To fix an angle in Sketchpad, you need to construct the angle in such a way that dragging cannot change its magnitude. For an arbitrary angle, the easiest way to do this is with the Transform menu.

Follow these steps:

  1. Place two points A and B in your sketch.
  2. Select point A and choose Transform | Mark Center. Point A becomes marked as the center of future rotations and dilations.
  3. Select point B and choose Transform | Rotate. In the Rotation dialog box, enter the fixed angle by which you wish to rotate.

Sketchpad constructs point B', which is the rotated image of B by your requested angle. Even if you drag A, B, or B', Sketchpad will maintain this angle's magnitude because you've defined B' to be the rotated image of B by this angle.

You can now construct rays or segments connecting A, B, and B' to incorporate the fixed angle into your sketch.